Question

8. The lateral surface area of a hollow cylinder is 4224 cm.
It is cut along its height and formed a rectangular sheet
of width 33 cm. Find the perimeter of rectangular sheet?
​

Answer 1

Answer:

Perimeter of rectangular sheet is 322 cm

Answer 2

$\color{red}\huge{\underline{\underline{GIVEN\dag}}}$

• $Lateral\:Surface\:Area(LSA)_{cylinder}=4224cm$
• $Width_{rectangle}=33cm$

$\color{red}\huge{\underline{\underline{SOLUTION\dag}}}$

We know that;

$LSA_{cylinder}=2\pi rh$

Where;

• h is height
• r is radius

$\implies 4224=2\pi rh$

$\implies rh=\frac{2112}{\pi}$

$\implies r=\frac{2112}{h\pi}.......(1)$

$Width=2\pi r$

$\implies 33=2\pi (\frac{2112}{h\pi})$[From (1)]

$\implies 33=2(\frac{2112}{h})$

$\implies h=\frac{4224}{33}$

$\therefore\color{blue} h=128cm$

Since,cylinder was converted into rectangle

$length=height$

$\therefore\color{blue} length=128cm$

But;We also know that;

$Perimeter_{rectangle}=2(l+b)$

$Perimeter_{rectangle}=2(128+33)$

$Perimeter_{rectangle}=2(161)$

$\therefore\boxed{\orange{Perimeter_{rectangle}=322cm}}$

HOPE THAT HELPS!!